Net Force - Revision history

YorickAndeweg: /* Main Idea */

2019-08-03T19:06:44Z

Main Idea

← Older revision		Revision as of 15:06, 3 August 2019
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	==Main Idea==		==Main Idea==

	The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the [[Vectors\|vector]] ~~sum~~ of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.		The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the [[Vectors\|vector sum]] of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.

	The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.		The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.

YorickAndeweg: /* Main Idea */

2019-08-03T19:06:29Z

Main Idea

← Older revision		Revision as of 15:06, 3 August 2019
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	==Main Idea==		==Main Idea==

	The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the ~~vector sum (see~~ [[Vectors]]) of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.		The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the [[Vectors\|vector]] sum of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.

	The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.		The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.

YorickAndeweg: /* Examples */

2019-07-07T18:26:27Z

Examples

← Older revision		Revision as of 14:26, 7 July 2019
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	When calculating net force, it is useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.		When calculating net force, it is useful to construct a free body diagram. A free body diagram is a physical representation of the external forces applied to a system. Often, arrows are used to represent forces. In this example, forces are displayed acting on a box.

	The first box is being suspended by a rope, so its free body diagram looks like this:		The first box is being suspended by a rope (but it is not quite at equilibrium), so its free body diagram looks like this:

	[[File:Net_force_wiki_4.PNG]]		[[File:Net_force_wiki_4.PNG]]

			What is the net force acting on this box?

			Solution:

	Assume that down is the negative y direction, and you can easily write vector representations of the forces and add them up to find the sum, which is the net force:		Assume that down is the negative y direction, and you can easily write vector representations of the forces and add them up to find the sum, which is the net force:
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	[[File:Net_force_wiki_5.PNG]]		[[File:Net_force_wiki_5.PNG]]

			What is the net force acting on this box?

			Solution:

	<math> Fnet = (0, 600, 0) </math>N<math> + (0, -800, 0) </math>N<br>		<math> Fnet = (0, 600, 0) </math>N<math> + (0, -800, 0) </math>N<br>
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	[[File:Net_force_wiki_6.PNG]]		[[File:Net_force_wiki_6.PNG]]

			What is the net force acting on this box?

			Solution:

	<math> Fnet = (0, 50, 0) </math>N<math> + (0, -50, 0) </math>N<math> + (-20, 0, 0)</math>N<br>		<math> Fnet = (0, 50, 0) </math>N<math> + (0, -50, 0) </math>N<math> + (-20, 0, 0)</math>N<br>

YorickAndeweg: /* 3. (Middling) */

2019-07-07T18:24:46Z

3. (Middling)

← Older revision		Revision as of 14:24, 7 July 2019
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	===3. (Middling)===		===3. (Middling)===
	There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).		There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

			Solution:

	Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)		Let <math> f </math> = force of friction, <math> W </math> = weight of the object, and <math> N = </math> normal force. (The pictures are not to scale.)

YorickAndeweg: /* References */

2019-06-07T02:22:00Z

References

← Older revision		Revision as of 22:22, 6 June 2019
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	Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf <br>		Stinner, Arthur. "The story of force: from Aristotle to Einstein." Physics Education. 1994. Web. 30 Nov 2015. http://www.arthurstinner.com/stinner/pdfs/1994-storyofforce.pdf <br>
	[[Category:~~Which Category did you place this in?~~]]
			[[Category: Interactions]]

YorickAndeweg: /* A Mathematical Model */

2019-06-04T18:25:50Z

A Mathematical Model

← Older revision		Revision as of 14:25, 4 June 2019
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	Sometimes the individual force vectors are simply given in component form. In this case, recall that to add the force vectors, their corresponding components of the vectors should be added to yield the components of the resultant vector.		Sometimes the individual force vectors are simply given in component form. In this case, recall that to add the force vectors, their corresponding components of the vectors should be added to yield the components of the resultant vector.

	At least as often, the individual force vectors have known magnitudes and directions. In this case, coordinate axes should be chosen and the forces should be decomposed into components along those axes. If it is possible to predict the direction of the net force using physical intuition, the axes should be chosen so that one of them is parallel to this net force. Otherwise, The axes should be chosen so that as many forces as possible are parallel to them an axis, reducing the need to decompose them.		At least as often, the individual force vectors are not given in component form but have known magnitudes and directions. In this case, coordinate axes should be chosen and the forces should be decomposed into components along those axes. If it is possible to predict the direction of the net force using physical intuition, the axes should be chosen so that one of them is parallel to this net force. Otherwise, The axes should be chosen so that as many forces as possible are parallel to them an axis, reducing the need to decompose them.

	Recall that some forces, such as tension and the normal force, do not have readily available magnitudes; their magnitudes must be found based on the magnitudes of other forces.		Recall that some forces, such as tension and the normal force, do not have readily available magnitudes; their magnitudes must be found based on the magnitudes of other forces.

YorickAndeweg: /* Examples */

2019-05-29T16:14:48Z

Examples

← Older revision		Revision as of 12:14, 29 May 2019
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	<math>\vec{F}_{net}</math> = <60,-70,0)N + <20,10,0>N = <80,-60,0>N		<math>\vec{F}_{net}</math> = <60,-70,0)N + <20,10,0>N = <80,-60,0>N

	===3. (~~Intermediate~~)===		===3. (Middling)===
	There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).		There is a box, small enough to represented as a point, sitting on a slope inclined twenty degrees with respect to the horizontal. If its mass is 10 kg, what does the magnitude of the force of static friction (pointing up the hill) have to be for net force to be zero? In that case, what is the magnitude of the normal force? (All forces are measured in newtons, and the acceleration due to gravity <math> = g = 9.8</math> <math>m/(s^2) </math>).

YorickAndeweg: /* A Computational Model */

2019-05-28T21:53:51Z

A Computational Model

← Older revision		Revision as of 17:53, 28 May 2019
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	===A Computational Model===		===A Computational Model===

	Fortunately, vector addition is very easy in computer ~~programs~~. As long as the individual forces acting on a particle are calculated as vectors, when they are added together, ~~the program~~ will add their components to find the resultant vector.		Fortunately, vector addition is very easy in computer programming languages such as vPython. As long as the individual forces acting on a particle are calculated as vectors, when they are added together, vPython will add their components to find the resultant vector.

	Finding the net force is an essential part of the [[Iterative Prediction]] process, which is used in most physics simulations. Below is an excerpt from a vPython program that uses iterative prediction to simulate the motion of a ball on a spring. The seven lines shown are responsible for the three steps of iterative prediction.		Finding the net force is an essential part of the [[Iterative Prediction]] process, which is used in most physics simulations. Below is an excerpt from a vPython program that uses iterative prediction to simulate the motion of a ball on a spring. The seven lines shown are responsible for the three steps of iterative prediction.

YorickAndeweg: /* Main Idea */

2019-05-28T20:26:50Z

Main Idea

← Older revision		Revision as of 16:26, 28 May 2019
Line 3:		Line 3:
	==Main Idea==		==Main Idea==

	The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the vector sum (see [[Vectors]] of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.		The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the vector sum (see [[Vectors]]) of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.

	The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.		The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.

YorickAndeweg: /* Main Idea */

2019-05-28T20:26:40Z

Main Idea

← Older revision		Revision as of 16:26, 28 May 2019
Line 3:		Line 3:
	==Main Idea==		==Main Idea==

	The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the vector sum of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.		The net force acting on a system (such as a particle, collection of particles, or rigid body) is defined as the vector sum (see [[Vectors]] of all of the forces acting on the system. People are interested in net force because a net force acting on a system affects its motion. More specifically, a nonzero net force causes the system's [[Linear Momentum]] to change over time in the direction of the net force, as described by [[Newton's Second Law: the Momentum Principle]]. For a system of constant mass, this change in momentum takes the form of [[Acceleration]] in the direction of the net force. Conversely, a net force of 0 acting on a system means that, according to Newton's Second Law, the system is travelling with a constant momentum. For a system of constant mass, this means that the system is travelling at constant speed, which may be zero or nonzero. The fact that motion is possible with a net force of 0 may be be counter-intuitive, but recall that [[Newton's First Law]] states that objects in motion stay in motion unless a (nonzero net) force acts on it. For example, consider a rock thrown in empty space. It will travel at a constant speed in a straight line forever unless it encounters something that can exert a force on it.

	The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.		The effects of a net force do not depend on the forces comprising it. For example, if the forces <math> f_1 = < 1, 1, 0 > </math> N and <math> f_1 = < 1, -1, 0 > </math> N act on a system, the net force would be <math> F_{net} = < 1, 0, 0 > </math> N. Similarly, if the forces <math> f_1 = < 2, 0, 0 > </math> N and <math> f_1 = < -1, 0, 0 > </math> N act on a system, the net force would also be <math> F_{net} = < 1, 0, 0 > </math> N. In both cases, the net force is the same, so momentum of the system will be affected in the same way for both net forces.